[throwaway2245]

In this case, the researchers admit and indicate they are doing multiple tests, but have not then done a multiple testing correction.

That's not even really a "p-hack" (where you hide that you have done multiple tests, in order to avoid a multiple testing correction and to report only the positive results): it's simply a p-mistake.

What they have said is statistically incorrect, judged on its own merits. Their conclusion is not supported by the research they have done.